# Generalized Linear Bandits with Limited Adaptivity

arXiv: https://arxiv.org/abs/2404.06831 · HTML: https://mlsanity.com/paper/2404.06831/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 10 Apr 2024.

## Builds on (most cited first, 13 of 13)

- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Improved Optimistic Algorithms for Logistic Bandits](https://mlsanity.com/paper/2002.07530/) (2020)
- [Bypassing the Monster: A Faster and Simpler Optimal Algorithm for Contextual Bandits under Realizability](https://mlsanity.com/paper/2003.12699/) (2020)
- [Batched Multi-armed Bandits Problem](https://mlsanity.com/paper/1904.01763/) (2019)
- [Scalable Generalized Linear Bandits: Online Computation and Hashing](https://mlsanity.com/paper/1706.00136/) (2017)
- [Sequential Batch Learning in Finite-Action Linear Contextual Bandits](https://mlsanity.com/paper/2004.06321/) (2020)
- [Instance-Wise Minimax-Optimal Algorithms for Logistic Bandits](https://mlsanity.com/paper/2010.12642/) (2020)
- [Linear Bandits with Limited Adaptivity and Learning Distributional Optimal Design](https://mlsanity.com/paper/2007.01980/) (2020)
- [Jointly Efficient and Optimal Algorithms for Logistic Bandits](https://mlsanity.com/paper/2201.01985/) (2022)
- [Dynamic Batch Learning in High-Dimensional Sparse Linear Contextual Bandits](https://mlsanity.com/paper/2008.11918/) (2020)
- [Algorithms for Non-Stationary Generalized Linear Bandits](https://mlsanity.com/paper/2003.10113/) (2020)
- [Improved Regret Bounds of (Multinomial) Logistic Bandits via Regret-to-Confidence-Set Conversion](https://mlsanity.com/paper/2310.18554/) (2023)
- [An Experimental Design Approach for Regret Minimization in Logistic Bandits](https://mlsanity.com/paper/2202.02407/) (2022)

## Built on by (most cited first, 22 of 22)

- [A Unified Confidence Sequence for Generalized Linear Models, with Applications to Bandits](https://mlsanity.com/paper/2407.13977/) (2024)
- [Generalized Linear Bandits: Almost Optimal Regret with One-Pass Update](https://mlsanity.com/paper/2507.11847/) (2025)
- [Improved Online Confidence Bounds for Multinomial Logistic Bandits](https://mlsanity.com/paper/2502.10020/) (2025)
- [Nearly Optimal Algorithms for Contextual Dueling Bandits from Adversarial Feedback](https://mlsanity.com/paper/2404.10776/) (2024)
- [Neural Logistic Bandits](https://mlsanity.com/paper/2505.02069/) (2025)
- [Generalized Kernelized Bandits: A Novel Self-Normalized Bernstein-Like Dimension-Free Inequality and Regret Bounds](https://mlsanity.com/paper/2508.01681/) (2025)
- [Efficient Algorithms for Logistic Contextual Slate Bandits with Bandit Feedback](https://mlsanity.com/paper/2506.13163/) (2025)
- [Achieving Limited Adaptivity for Multinomial Logistic Bandits](https://mlsanity.com/paper/2508.03072/) (2025)
- [Provable Anytime Ensemble Sampling Algorithms in Nonlinear Contextual Bandits](https://mlsanity.com/paper/2510.10730/) (2025)
- [Practical and Optimal Algorithm for Linear Contextual Bandits with Rare Parameter Updates](https://mlsanity.com/paper/2606.00984/) (2026)
- [Preference Learning with Response Time: Robust Losses and Guarantees](https://mlsanity.com/paper/2505.22820/) (2025)
- [Shuffle and Joint Differential Privacy for Generalized Linear Contextual Bandits](https://mlsanity.com/paper/2602.00417/) (2026)
- [A Jointly Efficient and Optimal Algorithm for Heteroskedastic Generalized Linear Bandits with Adversarial Corruptions](https://mlsanity.com/paper/2602.10971/) (2026)
- [Few Batches or Little Memory, But Not Both: Simultaneous Space and Adaptivity Constraints in Stochastic Bandits](https://mlsanity.com/paper/2603.13742/) (2026)
- [Logistic Bandits with tildeO(√dT) Regret without Context Diversity Assumptions](https://mlsanity.com/paper/2604.22161/) (2026)
- [Generalized Linear Bandits with Memory](https://mlsanity.com/paper/2608.15848/) (2026)
- [Stochastic Matching Bandits with Rare Optimization Updates](https://mlsanity.com/paper/2509.04194/) (2025)
- [Exploration via Feature Perturbation in Contextual Bandits](https://mlsanity.com/paper/2510.17390/) (2025)
- [Nonstationary Generalized Linear Bandits with Discounted Online Mirror Descent](https://mlsanity.com/paper/2605.25590/) (2026)
- [Contextual Slate GLM Bandits with Limited Adaptivity](https://mlsanity.com/paper/2606.31449/) (2026)
- [Nonlinear Bandit](https://mlsanity.com/paper/2607.07304/) (2026)
- [Memory--Batch Tradeoffs in Lipschitz Bandits](https://mlsanity.com/paper/2608.07922/) (2026)

## Abstract (arXiv)

We study the generalized linear contextual bandit problem within the constraints of limited adaptivity. In this paper, we present two algorithms, textttB-GLinCB and textttRS-GLinCB, that address, respectively, two prevalent limited adaptivity settings. Given a budget M on the number of policy updates, in the first setting, the algorithm needs to decide upfront M rounds at which it will update its policy, while in the second setting it can adaptively perform M policy updates during its course. For the first setting, we design an algorithm textttB-GLinCB, that incurs tildeO(√T) regret when M = Omega( loglog T ) and the arm feature vectors are generated stochastically. For the second setting, we design an algorithm textttRS-GLinCB that updates its policy tildeO(log2 T) times and achieves a regret of tildeO(√T) even when the arm feature vectors are adversarially generated. Notably, in these bounds, we manage to eliminate the dependence on a key instance dependent parameter kappa, that captures non-linearity of the underlying reward model. Our novel approach for removing this dependence for generalized linear contextual bandits might be of independent interest.